非線性微分方程摘要翻譯

1、<p>　　With the development of modern applied science and technology, applying calculus equation model to demonstrate natural phenomenon and engineering scientific issues has gradually become one of the most importan

2、t methods for scientific researches, and thus the processing and solution approach of calculus equation is essential for further studying and discussing the above issues.</p><p>　　So far, theory and method o

3、f non-linear differential equation have already become important mathematic tools to study and solve other scientific-technological problems. However, the huge difficulty when solving non-linear differential equation, es

4、pecially for the exact solution, stimulates people attempting to solve by various methods, the effective one of which is the vatiational literation method.</p><p>　　This context applied the variational liter

5、ation method to solve the initial value problem of first-order non-linear differential equation and boundary problem of second-order non-linear differential equation, respectively. This study has firstly tried to underst

6、and the variational literation method related concepts and characteristics, and subsequently calculated the approximate solution of some typical examples.</p><p>　　Key Words: Non-linear Differential Equation

7、; Variational Literation Method; Approximate Solution</p><p>　　隨著現(xiàn)代應用科學與技術的發(fā)展, 應用微分方程模型來描述自然現(xiàn)象和工程科學問題逐漸成為了重要的科學研究方法之一, 而相應的微分方程的處理和解法對于深入研究和探討這些問題具有極其重要的意義.</p><p>　　目前, 非線性微分方程邊值問題中的理論和方法已成

8、為人們研究解決其他科學技術問題的重要數(shù)學工具. 但由于對非線性微分方程求解難度很大, 特別是精確解, 人們就嘗試各種方法對進行求解, 其中變分迭代法就是一種較為有效的方法. </p><p>　　本文將利用變分迭代法分別對一階非線性微分方程的初值問題以及二階非線性微分方程邊值問題求解. 先對變分迭代法的相關概念, 性質(zhì)等進行了解, 再應用典型例子進行近似解的計算.</p><p>　　關鍵